Step 1 :Identify the null and alternative hypotheses. The null hypothesis, \(H_{0}\), is that there is no correlation (\(\rho=0\)), and the alternative hypothesis, \(H_{1}\), is that there is a correlation (\(\rho\neq0\)).
Step 2 :Identify the correlation coefficient, \(r\). The correlation coefficient, \(r\), is given as 0.957, which is very close to 1. This indicates a strong positive linear correlation.
Step 3 :Identify the critical value(s). The critical r values are given as ±0.2680855. The correlation coefficient is much larger than these critical values, indicating that the correlation is statistically significant.
Step 4 :The p-value is given as 0.000, which is less than the significance level of 0.05, further supporting the claim of a significant correlation.
Step 5 :Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternative hypothesis.
Step 6 :Therefore, it appears that a measured chest size can be used to predict the weight of a bear.
Step 7 :Final Answer: The correlation coefficient, \(r\), is \(\boxed{0.957}\). There are two critical values at \(r= \pm \boxed{0.268}\). There is sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes. Therefore, it appears that a measured chest size can be used to predict the weight of a bear. We reject the null hypothesis and accept the alternative hypothesis.